/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 49 The Canadian Census. The Canadia... [FREE SOLUTION] | 91Ó°ÊÓ

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The Canadian Census. The Canadian government's decision to eliminate the mandatory long-form version of the census and to move these questions to an optional survey has many concerned. Many members of the business community and economists stressed the importance of the census data for crafting public policy. The minister of industry was given the task of defending the government's decision. In response to an argument that making the long form of the census voluntary would skew the data by eliminating the statistical randomness of the survey, the minister replied: "Wrong. Statisticians can ensure validity with a larger sample size." 36 Is the minister correct? If not, explain in simple terms the error in his statement.

Short Answer

Expert verified
The minister is incorrect; a larger sample can't replace the need for randomness, which ensures unbiased data.

Step by step solution

01

Understanding the Concern

The concern is that making the long form of the census voluntary would lead to biased data and not truly represent the population because it would not be randomly sampled. This absence of randomness can skew results, as certain groups might be over or under-represented depending on who chooses to respond.
02

Analyzing the Minister's Claim

The minister claims that increasing the sample size can ensure validity, implying that a larger sample would counter the lack of randomness. However, this assumption overlooks a key aspect of data reliability, which is random selection, not just size.
03

Explaining the Error

The error in the minister's statement is that simply increasing sample size does not compensate for a lack of random sampling. When samples are voluntary, they introduce self-selection bias, meaning some groups may be more or less likely to respond, resulting in a non-representative sample.
04

Importance of Random Sampling

For data to be valid and unbiased, the sample must be randomly selected from the population. Random sampling reduces the chances of bias by ensuring every individual has an equal chance to be selected, something that is compromised when participation is voluntary.
05

Conclusion

The minister's statement overlooks the fundamental need for randomness in sampling. Simply increasing the number of responses does not counteract the biases introduced by voluntary participation, which can result in unrepresentative data.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Random Sampling
Random sampling is a critical concept in statistical analysis. It ensures that every member of a population has an equal chance of being selected. This is important because it minimizes potential biases and allows the sample to more accurately reflect the whole population.

In simple terms, imagine you have a jar full of mixed candies. If you want a sample that truly represents all types of candy, you need to select them randomly, otherwise, you might just end up with all the chocolates, and none of the gummies. Similarly, if a government survey randomly selects its participants, the results can be more trusted to reflect the entire population's views.

Random sampling is the backbone of creating reliable data. Without it, as in voluntary surveys, data can become skewed because people who choose to respond may have different characteristics than those who do not. This is why the minister's claim that increasing sample sizes can ensure validity is fundamentally flawed. Without randomness, the data might still not represent the population accurately, regardless of how many people respond.
Self-selection Bias
Self-selection bias occurs when individuals select themselves into a group, causing a biased sample in a study. This type of bias can significantly affect the outcomes and reliability of survey data.

When people have the option to choose whether or not to participate, certain groups may be more likely to respond. For example, people who feel strongly about an issue or have more time might be overrepresented, while less interested individuals might ignore the survey.

In the case of a voluntary census, this self-selection bias becomes a real issue. This can lead to skewed results and an unrepresentative sample, because it doesn't accurately capture the population's range of views and characteristics. Increasing the sample size doesn't help in this scenario because the fundamental issue is the lack of random selection, thus the data may still miss key segments of the population.
Census Data Accuracy
The accuracy of census data is crucial to forming effective public policies and understanding demographic changes. Accurate data allows governments and researchers to allocate resources effectively, plan for educational needs, and develop healthcare services.

Census data is collected to capture a complete picture of the population, including age, income, employment, and many other factors. When collecting this data, accuracy is paramount for ensuring that all groups are represented proportionally.

Therefore, mandatory participation in census surveys is often emphasized to maintain accuracy. If the survey becomes voluntary, it introduces the risk of skewed data due to self-selection bias and lack of random sampling. This can result in misrepresented data, which could lead to misguided policy decisions and inefficient allocation of resources.

Maintaining the accuracy of census data is why many experts opposed changing to a voluntary format. The concern is that the voluntary approach compromises the integrity of the data collected, reflecting poorly on population representation.

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Most popular questions from this chapter

The National Health and Nutrition Examination Study (NHANES) had a random sample of 9317 participants recall their diet over the past 24 hours. The information in this sample was used in a recent study that found that, on average, \(57.9 \%\) of the calories eaten by participants were obtained from ultra-processed foods that include substances not used in culinary preparations, such as flavors, colors, sweeteners, emulsifiers, and other additives. One of the limitations of the study reported by the authors was the dependence on the dietary recall of individuals. \(\underline{20}\) The authors were concerned with a. response bias. b. undercoverage. c. overstratification.

Universal Health Care. In 2019, a Monmouth University poll and an NBC News/Wall Street Journal poll each asked a nationwide sample about their views on universal health care. \(\frac{12}{}\) Here are the two questions: Question A: Do you favor or oppose creating a universal health care system in America? Question B: Would you favor or oppose a single payer health care system in which all Americans would get their health insurance from one government plan that is financed in part by taxes? One of these questions had \(58 \%\) responding favor, and the other question had only \(44 \%\) responding favor. Which wording is slanted toward a more negative response on universal health care? Why?

A Twitter Poll. In September 2019, ProgressPolls asked the question "Do you think the Democrats have a valid reason for wanting to impeach Trump?" Of the 1437 votes cast, \(91 \%\) said no. This poll was a Twitter poll. A CNN random digit dialing telephone poll of 1003 respondents in September 2019 asked the question "In your view, why do most Democrats in Congress support impeachment of Donald Trump?" Thirty eight percent responded "Because they are out to get Donald Trump at all costs." Explain to someone who knows no statistics why the two polls can give such widely differing results and which poll is likely to be more reliable.

Cluster Sampling. Cluster sampling begins by dividing the population into separate groups, or clusters. An SRS of the clusters is selected, and individuals in the cluster are sampled. If all the individuals in a cluster are sampled, this is called one-stage cluster sampling. If a random sample of individuals in a cluster is sampled, this is called two-stage sampling. Cluster sampling can be convenient when the individuals in a cluster are easily sampled as a group, such as all people in a neighborhood for a door-to- door survey. Here is a simple example of one-stage cluster sampling. All students at a small college are required to live in dormitories. There are 25 such dormitories on campus, each with 30 students. a. To select a cluster sample of 150 students, do the following. Label the dormitories from 01 to 25. Choose an SRS of 5 dormitories from the list of the 25. If you use Table \(\mathrm{B}\), enter the table at line 121 and indicate which dormitories you selected. Your cluster sample is the 150 students in these dormitories. b. How many dormitories would you have to sample if you wanted a sample of 100 students?

Nonresponse. Exercise \(8.10\) discusses the Pew Research Center survey Teens, Social Media \(\&\) Technology conducted in the spring of 2018 . The report mentions that 743 teens completed the survey and that the response rate for teens was \(18 \% .27\) Approximately how many teens must have been recruited for the survey for a response rate of \(18 \% ?\)

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